Explanation

(c) According to Laplace, the speed of sound in a gas is
$v = \sqrt{\frac{\gamma p}{d}} = \sqrt{\frac{\gamma RT}{M}}$
Where R is gas constant, T the temperature and M the molecular weight.
For monatomic gas helium, $\gamma_{1} = \frac{5}{3},M_{1} = 4$
For diatomic gas nitrogen, $\gamma_{2} = \frac{7}{5},M_{2} = 28$
$\therefore\ \frac{v_{N_{2}}}{v_{H_{e}}} = \sqrt{\frac{\gamma_{1}M_{2}}{\gamma_{2}M_{1}}}$
$= \sqrt{\frac{5/3}{7/5} \times \frac{28}{4}} = \sqrt{\frac{5 \times 5}{3}} = \frac{5}{\sqrt{3}}$
Hence,
$\frac{{v_{h}}_{2}}{v_{He}} = \frac{\sqrt{3}}{5}$